{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T18:08:48Z","timestamp":1781374128874,"version":"3.54.1"},"reference-count":37,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T00:00:00Z","timestamp":1724889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The use of linear array pushbroom images presents a new challenge in photogrammetric applications when it comes to transforming object coordinates to image coordinates. To address this issue, the Best Scanline Search\/Determination (BSS\/BSD) field focuses on obtaining the Exterior Orientation Parameters (EOPs) of each individual scanline. Current solutions are often impractical for real-time tasks due to their high time requirements and complexities. This is because they are based on the Collinearity Equation (CE) in an iterative procedure for each ground point. This study aims to develop a novel BSD framework that does not need repetitive usage of the CE with a lower computational complexity. The Linear Regression Model (LRM) forms the basis of the proposed BSD approach and uses Simulated Control Points (SCOPs) and Simulated Check Points (SCPs). The proposed method is comprised of two main steps: the training phase and the test phase. The SCOPs are used to calculate the unknown parameters of the LR model during the training phase. Then, the SCPs are used to evaluate the accuracy and execution time of the method through the test phase. The evaluation of the proposed method was conducted using ten various pushbroom images, 5 million SCPs, and a limited number of SCOPs. The Root Mean Square Error (RMSE) was found to be in the order of ten to the power of negative nine (pixel), indicating very high accuracy. Furthermore, the proposed approach is more robust than the previous well-known BSS\/BSD methods when handling various pushbroom images, making it suitable for practical and real-time applications due to its high speed, which only requires 2\u20133 s of time.<\/jats:p>","DOI":"10.3390\/s24175594","type":"journal-article","created":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T03:40:39Z","timestamp":1724902839000},"page":"5594","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Linear Regression Approach for Best Scanline Determination in the Object to Image Space Transformation Using Pushbroom Images"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8274-6030","authenticated-orcid":false,"given":"Seyede Shahrzad","family":"Ahooei Nezhad","sequence":"first","affiliation":[{"name":"Department of Photogrammetry and Remote Sensing, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran 19967-15443, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4325-8741","authenticated-orcid":false,"given":"Mohammad Javad","family":"Valadan Zoej","sequence":"additional","affiliation":[{"name":"Department of Photogrammetry and Remote Sensing, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran 19967-15443, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7265-3866","authenticated-orcid":false,"given":"Fahimeh","family":"Youssefi","sequence":"additional","affiliation":[{"name":"Department of Photogrammetry and Remote Sensing, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran 19967-15443, Iran"},{"name":"Institute of Artificial Intelligence, Shaoxing University, 508 West Huancheng Road, Yuecheng District, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5165-1773","authenticated-orcid":false,"given":"Ebrahim","family":"Ghaderpour","sequence":"additional","affiliation":[{"name":"Department of Earth Sciences and CERI Research Centre, Sapienza University of Rome, P.le Aldo Moro, 5, 00185 Rome, Italy"},{"name":"Earth and Space Inc., Calgary, AB T3A 5B1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.5194\/isprs-annals-V-1-2020-89-2020","article-title":"Quantitative Assessment of the Projection Trajectory-Based Epipolarity Model and Epipolar Image Resampling for Linear-Array Satellite Images","volume":"5","author":"Gong","year":"2020","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_2","unstructured":"(2022, October 18). Gong New Methods for 3D Reconstructions Using High Resolution Satellite Data. Available online: http:\/\/elib.uni-stuttgart.de\/bitstream\/11682\/11470\/1\/PhD_thesis_Ke_Gong.pdf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"369","DOI":"10.5194\/isprsarchives-XL-1-W1-369-2013","article-title":"Geometric Correction of Airborne Linear Array Image Based on Bias Matrix","volume":"XL\u20131\/W1","author":"Wang","year":"2013","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Koduri, S. (2012, January 28\u201330). Modeling pushbroom scanning systems. Proceedings of the 2012 14th International Conference on Modelling and Simulation, UKSim 2012, Cambridge, UK.","DOI":"10.1109\/UKSim.2012.62"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1007\/s12583-015-0605-0","article-title":"Affine & scale-invariant heterogeneous pyramid features for automatic matching of high resolution pushbroom imagery from Chang\u2019e 2 satellite","volume":"27","author":"Yang","year":"2016","journal-title":"J. Earth Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Geng, X., Xu, Q., Lan, C., Hou, Y., Miao, J., and Xing, S. (2018, January 18\u201320). An Efficient Geometric Rectification Method for Planetary Linear Pushbroom Images Based on Fast Back Projection Algorithm. Proceedings of the 2018 Fifth International Workshop on Earth Observation and Remote Sensing Applications (EORSA), Xi\u2019an, China.","DOI":"10.1109\/EORSA.2018.8598644"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.14358\/PERS.72.11.1255","article-title":"Epipolar resampling of space-borne linear array scanner scenes using parallel projection","volume":"72","author":"Morgan","year":"2006","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/s11263-010-0349-3","article-title":"Plane-based calibration for linear cameras","volume":"91","author":"Roy","year":"2011","journal-title":"Int. J. Comput. Vis."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jannati, M., Zoej, M.J.V., and Mokhtarzade, M. (2017). Epipolar resampling of cross-track pushbroom satellite imagery using the rigorous sensor model. Sensors, 17.","DOI":"10.3390\/s17010129"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2018.01.008","article-title":"A novel approach for epipolar resampling of cross-track linear pushbroom imagery using orbital parameters model","volume":"137","author":"Jannati","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.isprsjprs.2011.01.002","article-title":"Epipolar resampling of linear pushbroom satellite imagery by a new epipolarity model","volume":"66","author":"Wang","year":"2011","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ahooei Nezhad, S.S., Valadan Zoej, M.J., Khoshelham, K., Ghorbanian, A., Farnaghi, M., Jamali, S., Youssefi, F., and Gheisari, M. (2024). Best Scanline Determination of Pushbroom Images for a Direct Object to Image Space Transformation Using Multilayer Perceptron. Remote Sens., 16.","DOI":"10.3390\/rs16152787"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6035","DOI":"10.1109\/TGRS.2015.2431434","article-title":"Automatic orthorectification of high-resolution optical satellite images using vector roads","volume":"53","author":"Fras","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e2019EA001014","DOI":"10.1029\/2019EA001014","article-title":"A Generic Pushbroom Sensor Model for Planetary Photogrammetry","volume":"7","author":"Geng","year":"2020","journal-title":"Earth Sp. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Habib, A.F., Bang, K.I., Kim, C.J., and Shin, S.W. (2006). True ortho-photo generation from high resolution satellite imagery. Lecture Notes in Geoinformation and Cartography, Springer.","DOI":"10.1007\/978-3-540-36998-1_49"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1080\/01431161.2022.2032459","article-title":"A novel inverse transformation algorithm for pushbroom TDI CCD imaging","volume":"43","author":"Jiang","year":"2022","journal-title":"Int. J. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"565","DOI":"10.14358\/PERS.81.7.565","article-title":"A fast and robust scan-line search algorithm for object-to-image projection of airborne pushbroom images","volume":"81","author":"Shen","year":"2015","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"17297","DOI":"10.3390\/rs71215883","article-title":"Toward high altitude airship ground-based boresight calibration of hyperspectral pushbroom imaging sensors","volume":"7","author":"Zhang","year":"2015","journal-title":"Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1029\/2019EA000646","article-title":"A Robust Ground-to-Image Transformation Algorithm and Its Applications in the Geometric Processing of Linear Pushbroom Images","volume":"6","author":"Geng","year":"2019","journal-title":"Earth Sp. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"129","DOI":"10.5194\/isprsarchives-XL-2-W2-129-2013","article-title":"Real time processing for epipolar resampling of linear pushbroom imagery based on the fast algorithm for best scan line searching","volume":"XL\u20132\/W2","author":"Geng","year":"2013","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.-ISPRS Arch."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3584","DOI":"10.1016\/j.asr.2021.06.046","article-title":"A fast non-iterative method for the object to image space best scanline determination of spaceborne linear array pushbroom images","volume":"68","author":"Nezhad","year":"2021","journal-title":"Adv. Sp. Res."},{"key":"ref_22","first-page":"347","article-title":"A New True Ortho-photo Generation Algorithm for High Resolution Satellite Imagery","volume":"26","author":"Bang","year":"2010","journal-title":"Korean J. Remote Sens."},{"key":"ref_23","first-page":"247","article-title":"Efficient orthoimage generation from ADS40 level 0 products","volume":"11","author":"Liu","year":"2007","journal-title":"J. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1109\/36.317439","article-title":"A Unified Solution for Digital Terrain Model and Orthoimage Generation from SPOT Stereopairs","volume":"31","author":"Chen","year":"1993","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.14358\/PERS.75.9.1059","article-title":"A fast approach to best scanline search of airborne linear pushbroom images","volume":"75","author":"Wang","year":"2009","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ijrefrig.2024.01.028","article-title":"Maximizing efficiency in solar ammonia\u2013water absorption refrigeration cycles: Exergy analysis, concentration impact, and advanced optimization with GBRT machine learning and FHO optimizer","volume":"161","author":"Alahmer","year":"2024","journal-title":"Int. J. Refrig."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Huang, R., Zheng, S., and Hu, K. (2018). Registration of aerial optical images with LiDAR data using the closest point principle and collinearity equations. Sensors, 18.","DOI":"10.3390\/s18061770"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1016\/j.asr.2014.12.018","article-title":"An optimized orbital parameters model for geometric correction of space images","volume":"55","author":"Safdarinezhad","year":"2015","journal-title":"Adv. Sp. Res."},{"key":"ref_29","unstructured":"Zoej, M.J.V. (1997). Photogrammetric Evaluation of Space Linear Array Imagery for Medium Scale Topographic Mapping. [Ph.D. Thesis, University of Glasgow]. Available online: https:\/\/theses.gla.ac.uk\/4777\/1\/1997zoejphd1.pdf."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"33","DOI":"10.4103\/jpcs.jpcs_8_18","article-title":"Linear regression analysis study","volume":"4","author":"Kumari","year":"2018","journal-title":"J. Pract. Cardiovasc. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hope, T.M.H. (2019). Linear regression. Machine Learning: Methods and Applications to Brain Disorders, Academic Press.","DOI":"10.1016\/B978-0-12-815739-8.00004-3"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"140","DOI":"10.38094\/jastt1457","article-title":"A Review on Linear Regression Comprehensive in Machine Learning","volume":"1","author":"Maulud","year":"2020","journal-title":"J. Appl. Sci. Technol. Trends"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.sbspro.2013.12.027","article-title":"A Study on Multiple Linear Regression Analysis","volume":"106","year":"2013","journal-title":"Procedia-Soc. Behav. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ghaderpour, E., Pagiatakis, S.D., and Hassan, Q.K. (2021). A survey on change detection and time series analysis with applications. Appl. Sci., 11.","DOI":"10.3390\/app11136141"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"e1524","DOI":"10.1002\/wics.1524","article-title":"Robust linear regression for high-dimensional data: An overview","volume":"13","author":"Filzmoser","year":"2021","journal-title":"Wiley Interdiscip. Rev. Comput. Stat."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.proeng.2012.09.545","article-title":"Modelling using polynomial regression","volume":"48","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_37","first-page":"731","article-title":"K-means clustering analysis and multiple linear regression model on household income in Malaysia","volume":"12","author":"Yee","year":"2023","journal-title":"IAES Int. J. Artif. Intell."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5594\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:44:46Z","timestamp":1760111086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,29]]},"references-count":37,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24175594"],"URL":"https:\/\/doi.org\/10.3390\/s24175594","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,29]]}}}